I have an observation I would like to share with you guys. I am modelling a 2D NASA airfoil at zero angle of attak (so that there is no separation!). (Mach = 0.05, Re = 1.44e6, chord = 4.089 ft). I have experimental data on this airfoil: Cl = 0.54 @ alpha = 0 deg.

Here is what I did:

I use RNG k-e model with standard wall function. According to the code, y+ range is within 35 - 350. I believe my mesh density is sufficient to capture all the flow structure. The procedure of my analysis is to gradually reduce the distance between the first node and the airfoil surface, while keeping the rest of the parameters constant (This means the overall node count in the entire model remains constant). y+ is gradually reducing, which makes sense, and the y+ values all around the airfoil for different cases still satisfy the 35 - 350 range. What I observed is my computed Cl deviates more (getting smaller) from the experimental data when the y+ values are gradually reduced.

I get the same trend when I try to refine the mesh around the airfoil.

In conclusion, computed Cl is closer to the experimental Cl if my y+ is bigger. My question is, is this the general trend? Normally when we do mesh dependency test, we expect the computed solution to get closer to the experimental result or exact solution (if available). However, this is not what I observed, which means a very serious thing, i.e. the notion of mesh dependency test guide me to a more incorrect computed solution. And the changes in computed result (in this case Cl computed) is big (not like a small change of .1% in Cl that I can ignore).

In case a bug free code, you should get closer to the exact solution when refining the mesh.

But getting closer to the experimental solution is another issue:

- the experiment is never fully 2-D - how is the model machined, ie. is your computed shape "exactly" the same as the one in experiments - freestream turbulence in the experiments - was the AOA really 0 or maybe 0.1 degrees in experiments? - ....

I know these issues are far more severe a lower Re than what you are dealing with but might still be valid.